Finite Group Databasebeta

← #104×C22⋊D43 #25112267

Subgroups — #104×C22⋊D43 #25112267

Order 11008.

1608 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C22⋊D43C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#104×D43C211yesmaximal, characteristic, complemented
4C42×C22⋊D43C211yesmaximal, characteristic, complemented
5#19135512C211yesmaximal, characteristic, complemented
6#19135421C211yesmaximal, characteristic, complemented
7#19135038C211yesmaximal, characteristic, complemented
8#19135035C211yesmaximal, characteristic, complemented
9#19134897C211yesmaximal, characteristic, complemented
10#19134894C211yesmaximal, characteristic, complemented
11#19134613C211yesmaximal, characteristic, complemented
12#19134539C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#104×Dic43C211yesmaximal, characteristic, complemented
15C22×#104×C43C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic, complemented
18#14583568C411yescharacteristic, complemented
19Q8×C22⋊D43C411yescharacteristic, complemented
20#14583560C411yescharacteristic, complemented
21#14583556C411yescharacteristic, complemented
22#14583548—21no—
23#14583548C411yescharacteristic, complemented
24#14583543—21no—
25#14583543C411yescharacteristic, complemented
26#14583537—21no—
27#14583537C411yescharacteristic, complemented
28D4×C22⋊D43—21no—
29D4×C22⋊D43C411yescharacteristic, complemented
30#14583445—21no—
31#14583445C2211yescharacteristic
32#14583410—21no—
33#14583410C2211yescharacteristic
34#14583406—21no—
35#14583406C2211yescharacteristic
36#41×Dic43C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×C42×D43C2211yescharacteristic, complemented
41#14582975—21no—
42#14582970—21no—
43#14582968—21no—
44C8×C22⋊D43—21no—
45#14582922C2211yescharacteristic, complemented
46C2×#13063253C2211yescharacteristic, complemented
47C2×#13063253C2211yescharacteristic, complemented
48C2×#13063252C2211yescharacteristic
49C2×#13063252C2211yescharacteristic
50C2×#13063252C2211yescharacteristic, complemented
51C2×#13063252C2211yescharacteristic, complemented
52C2×#13063251C2211yescharacteristic, complemented
53C2×#13063251C2211yescharacteristic, complemented
54#104×D43—24no—
55#14582863C2211yescharacteristic, complemented
56#14582862C2211yescharacteristic, complemented
57M16×Dic43C2211yescharacteristic, complemented
58C4×Dic43⋊C4—21no—
59C4×Dic43⋊C4C2211yescharacteristic, complemented
60C4×(C2×D43)⋊C4—21no—
61C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
62C4×C22⋊Dic43—21no—
63C4×C22⋊Dic43C2211yescharacteristic, complemented
64C42×Dic43C2211yescharacteristic, complemented
65#14582660C2211yescharacteristic, complemented
66#14582660C2211yescharacteristic, complemented
67#14582659C2211yescharacteristic, complemented
68#14582659C2211yescharacteristic, complemented
69C22×#41×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic, complemented
71C22×C42×C43C2211yescharacteristic, complemented
72C2×#104×C43—24no—
73C2×#104×C43C2211yescharacteristic
74C2×#104×C43C2211yescharacteristic
75C2×#104×C43C2211yescharacteristic, complemented
76C2×#104×C43C2211yescharacteristic, complemented
77C2×#10621902C2×C411yescharacteristic, complemented
78C2×#10621898—21no—
79C2×#10621898C2311yescharacteristic
80C2×#10621900—21no—
81C2×#10621900C2×C411yescharacteristic, complemented
82#41×D43—22no—
83#41×D43—22no—
84#41×D43—41no—
85#41×D43—41no—
86C2×Q8×D43C2×C411yescharacteristic, complemented
87C22×C22⋊D43—21no—
88C22×C22⋊D43D411yescharacteristic
89C2×D4×D43—21no—
90C2×D4×D43C2×C411yescharacteristic, complemented
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43C2311yescharacteristic
94C2×#10621877C2311yescharacteristic
95C2×#10621877C2311yescharacteristic
96C2×#10621872—21no—
97M16×D43—22no—
98M16×D43—41no—
99C2×C8×D43—21no—
100#13063323—21no—
101#13063323C2×C411yescharacteristic, complemented
102#13063321—21no—
103#13063321C2×C411yescharacteristic, complemented
104#13063314—21no—
105#13063314C2×C411yescharacteristic, complemented
106#13063312—21no—
107#13063312C2×C411yescharacteristic, complemented
108#13063308—21no—
109#13063308—21no—
110#13063308—21no—
111#13063306—21no—
112#13063306—21no—
113#13063306—21no—
114#13063304—21no—
115#13063304—21no—
116#13063304C2×C411yescharacteristic, complemented
117#13063304C2×C411yescharacteristic, complemented
118#13063301—21no—
119#13063301—21no—
120#13063301C2×C411yescharacteristic, complemented
121#13063301C2×C411yescharacteristic, complemented
122#13063299—21no—
123#13063299—21no—
124#13063299C2×C411yescharacteristic, complemented
125#13063299C2×C411yescharacteristic, complemented
126#13063297—21no—
127#13063297—21no—
128#13063297—21no—
129#13063297—21no—
130#13063297—21no—
131#13063297—21no—
132#13063296—21no—
133#13063296—21no—
134#13063296C2×C411yescharacteristic, complemented
135#13063296C2×C411yescharacteristic, complemented
136#13063294—21no—
137#13063294—21no—
138#13063294—21no—
139#13063293—21no—
140#13063293—21no—
141#13063293—21no—
142Q8×Dic43C2×C411yescharacteristic, complemented
143Q8×Dic43C2×C411yescharacteristic, complemented
144D4×Dic43—21no—
145D4×Dic43—21no—
146D4×Dic43C2×C411yescharacteristic, complemented
147D4×Dic43C2×C411yescharacteristic, complemented
148C4×C22⋊D43—28no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43—21no—
151C4×C22⋊D43—21no—
152C4×C22⋊D43—21no—
153C4×C22⋊D43—21no—
154C4×C22⋊D43—21no—
155C4×C22⋊D43—21no—
156C4×C22⋊D43—21no—
157C4×C22⋊D43—21no—
158C4×C22⋊D43—21no—
159C4×C22⋊D43C2×C411yescharacteristic
160C4×C22⋊D43C2×C411yescharacteristic
161C4×C22⋊D43C2×C411yescharacteristic
162C4×C22⋊D43C2×C411yescharacteristic
163C4×C22⋊D43D411yescharacteristic
164C4×C22⋊D43D411yescharacteristic
165C4×C22⋊D43D411yescharacteristic
166C4×C22⋊D43D411yescharacteristic
167#13063284—21no—
168#13063284C2311yescharacteristic
169C2×Dic43⋊C4—21no—
170C2×Dic43⋊C4—21no—
171C2×Dic43⋊C4D411yescharacteristic
172C2×C22⋊Dic43—21no—
173C2×C22⋊Dic43—21no—
174C2×C22⋊Dic43D411yescharacteristic
175C2×(C2×D43)⋊C4—21no—
176C2×(C2×D43)⋊C4—21no—
177C2×(C2×D43)⋊C4D411yescharacteristic
178C2×C4×Dic43—21no—
179C2×C4×Dic43—21no—
180C2×C4×Dic43—21no—
181C2×C4×Dic43—21no—
182C2×C4×Dic43C2311yescharacteristic
183C2×C4×Dic43C2311yescharacteristic
184C2×C4×Dic43C2311yescharacteristic
185C42×D43—22no—
186C42×D43—41no—
187Dic43⋊C8—21no—
188Dic43⋊C8—21no—
189#13063253—22no—
190#13063253—41no—
191#13063252—22no—
192#13063252—22no—
193#13063252—41no—
194#13063252—41no—
195#13063251—22no—
196#13063251—41no—
197C22⋊(C43⋊C8)—21no—
198C22⋊(C43⋊C8)—21no—
199(C2×D43)⋊C8—21no—
200(C2×D43)⋊C8—21no—
201#13063235—21no—
202C8×Dic43—21no—
203C43⋊#95—21no—
204C43⋊#95—21no—
205C43⋊#95—21no—
206C2×#41×C43—21no—
207C2×#41×C43—21no—
208C2×#41×C43—22no—
209C2×#41×C43—22no—
210C2×#41×C43—41no—
211C2×#41×C43—41no—
212C2×#41×C43C2×C411yescharacteristic, complemented
213C2×#41×C43C2×C411yescharacteristic, complemented
214C2×#41×C43C2311yescharacteristic
215C2×#41×C43C2311yescharacteristic
216C22×Q8×C43C2×C411yescharacteristic, complemented
217C22×D4×C43—21no—
218C22×D4×C43C2×C411yescharacteristic, complemented
219C23×C4×C43—21no—
220C23×C4×C43—21no—
221C23×C4×C43C2311yescharacteristic
222C2×M16×C43—21no—
223C2×M16×C43—22no—
224C2×M16×C43—41no—
225C2×M16×C43C2311yescharacteristic
226C2×M16×C43C2311yescharacteristic
227C22×C8×C43—21no—
228C2×C42×C43—22no—
229C2×C42×C43—21no—
230C2×C42×C43—41no—
231C2×C42×C43C2311yescharacteristic
232C2×C42×C43C2311yescharacteristic
233#104×C43—22no—
234#104×C43—22no—
235#104×C43—22no—
236#104×C43D414yescomplemented
237C24×C43—21no—
238C24×C43C2×D411yescharacteristic
239C23×D43—21no—
240C23×D43C2×D411yescharacteristic
241#41×C43—21no—
242#41×C43—21no—
243#41×C43—22no—
244#41×C43—22no—
245#41×C43—21no—
246#41×C43—21no—
247#41×C43—21no—
248#41×C43—21no—
249#41×C43—42no—
250#41×C43—42no—
251#41×C43—41no—
252#41×C43—41no—
253#41×C43—42no—
254#41×C43—42no—
255#41×C43C2×D412yes—
256#41×C43#4112yes—
257C2×Q8×C43—21no—
258C2×Q8×C43—22no—
259C2×Q8×C43—41no—
260C2×Q8×C43C22×C411yescharacteristic
261C2×Q8×C43C22×C411yescharacteristic
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—22no—
268C2×D4×C43—42no—
269C2×D4×C43—42no—
270C2×D4×C43—41no—
271C2×D4×C43C22×C411yescharacteristic
272C2×D4×C43C22×C411yescharacteristic
273C22×C4×C43—21no—
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—21no—
277C22×C4×C43—21no—
278C22×C4×C43—24no—
279C22×C4×C43—21no—
280C22×C4×C43—21no—
281C22×C4×C43—21no—
282C22×C4×C43—21no—
283C22×C4×C43—21no—
284C22×C4×C43—21no—
285C22×C4×C43—42no—
286C22×C4×C43—42no—
287C22×C4×C43—42no—
288C22×C4×C43—42no—
289C22×C4×C43C22×C411yescharacteristic
290C22×C4×C43C22×C411yescharacteristic
291C22×C4×C43C2×D411yescharacteristic
292C22×C4×C43C2×D411yescharacteristic
293C22×C4×C43C2×D411yescharacteristic
294C22×C4×C43C2411yescharacteristic
295C2×C22⋊D43—24no—
296C2×C22⋊D43—21no—
297C2×C22⋊D43—21no—
298C2×C22⋊D43—21no—
299C2×C22⋊D43—21no—
300C2×C22⋊D43—21no—
301C2×C22⋊D43—21no—
302C2×C22⋊D43—21no—
303C2×C22⋊D43—21no—
304C2×C22⋊D43—21no—
305C2×C22⋊D43—44no—
306C2×C22⋊D43C22⋊C411yescharacteristic
307C2×C22⋊D43C22⋊C411yescharacteristic
308C2×C22⋊D43C22⋊C411yescharacteristic
309C2×C22⋊D43C22⋊C411yescharacteristic
310C22×Dic43—21no—
311C22×Dic43—21no—
312C22×Dic43—21no—
313C22×Dic43—21no—
314C22×Dic43—21no—
315C22×Dic43C2×D411yescharacteristic
316C22×Dic43C2×D411yescharacteristic
317C22×Dic43C2×D411yescharacteristic
318#10621902—22no—
319#10621902—41no—
320Q8×D43—22no—
321Q8×D43—41no—
322#10621900—22no—
323#10621900—41no—
324#10621900—42no—
325#10621900—42no—
326D4×D43—22no—
327D4×D43—42no—
328D4×D43—42no—
329D4×D43—41no—
330#10621898—21no—
331#10621898—21no—
332#10621898—21no—
333#10621898—21no—
334#10621898—42no—
335#10621898—42no—
336C2×D172—21no—
337C2×D172C22×C411yescharacteristic
338C2×C4×D43—21no—
339C2×C4×D43—21no—
340C2×C4×D43—21no—
341C2×C4×D43—21no—
342C2×C4×D43—24no—
343C2×C4×D43—21no—
344C2×C4×D43—21no—
345C2×C4×D43—21no—
346C2×C4×D43—42no—
347C2×C4×D43—42no—
348C2×C4×D43—42no—
349C2×C4×D43—42no—
350C2×C4×D43C22×C411yescharacteristic
351C2×C4×D43C22×C411yescharacteristic
352C2×C4×D43C2×D411yescharacteristic
353C2×C4×D43C2×D411yescharacteristic
354C2×Dic86—21no—
355C2×Dic86C22×C411yescharacteristic
356M16×C43—21no—
357M16×C43—21no—
358M16×C43—21no—
359M16×C43—42no—
360M16×C43C2×D412yescomplemented
361C2×C8×C43—21no—
362C2×C8×C43—21no—
363C2×C8×C43—42no—
364C42×C43—21no—
365C42×C43—21no—
366C42×C43—21no—
367C42×C43—42no—
368C42×C43C2×D412yescomplemented
369C22⋊Dic43—24no—
370C22⋊Dic43—21no—
371C22⋊Dic43—21no—
372C22⋊Dic43—21no—
373C22⋊Dic43—21no—
374C22⋊Dic43—21no—
375C22⋊Dic43—21no—
376C22⋊Dic43—21no—
377C22⋊Dic43—21no—
378C22⋊Dic43—21no—
379C22⋊Dic43C22⋊C411yescharacteristic
380C22⋊Dic43C22⋊C411yescharacteristic
381C22⋊Dic43C22⋊C411yescharacteristic
382C22⋊Dic43C22⋊C411yescharacteristic
383(C2×D43)⋊C4—24no—
384(C2×D43)⋊C4—21no—
385(C2×D43)⋊C4—21no—
386(C2×D43)⋊C4—21no—
387(C2×D43)⋊C4—21no—
388(C2×D43)⋊C4—21no—
389(C2×D43)⋊C4—21no—
390(C2×D43)⋊C4C22⋊C411yescharacteristic
391(C2×D43)⋊C4C22⋊C411yescharacteristic
392(C2×D43)⋊C4C22⋊C411yescharacteristic
393(C2×D43)⋊C4C22⋊C411yescharacteristic
394C4⋊Dic43—21no—
395C4⋊Dic43—21no—
396C4⋊Dic43C22×C411yescharacteristic
397C4⋊Dic43C22×C411yescharacteristic
398Dic43⋊C4—24no—
399Dic43⋊C4—21no—
400Dic43⋊C4—21no—
401Dic43⋊C4—21no—
402Dic43⋊C4—21no—
403Dic43⋊C4—21no—
404Dic43⋊C4—21no—
405Dic43⋊C4C22⋊C411yescharacteristic
406Dic43⋊C4C22⋊C411yescharacteristic
407Dic43⋊C4C22⋊C411yescharacteristic
408Dic43⋊C4C22⋊C411yescharacteristic
409C4×Dic43—24no—
410C4×Dic43—21no—
411C4×Dic43—21no—
412C4×Dic43—21no—
413C4×Dic43—21no—
414C4×Dic43—21no—
415C4×Dic43—21no—
416C4×Dic43—21no—
417C4×Dic43—42no—
418C4×Dic43—42no—
419C4×Dic43C22×C411yescharacteristic
420C4×Dic43C22×C411yescharacteristic
421C4×Dic43C2×D411yescharacteristic
422C4×Dic43C2×D411yescharacteristic
423#10621877—21no—
424#10621877—21no—
425#10621877—21no—
426#10621877—21no—
427C2×C43⋊C8—21no—
428C2×C43⋊C8—21no—
429#10621872—42no—
430C8×D43—42no—
431C23×C43—21no—
432C23×C43—21no—
433C23×C43—21no—
434C23×C43—22no—
435C23×C43—21no—
436C23×C43—41no—
437C23×C43—42no—
438C23×C43—42no—
439C23×C43—81no—
440C23×C43C2×C22⋊C411yescharacteristic
441C23×C43C2×C22⋊C411yescharacteristic
442C23×C43C22×D411yescharacteristic
443C22×D43—21no—
444C22×D43—21no—
445C22×D43—22no—
446C22×D43—21no—
447C22×D43—41no—
448C22×D43—42no—
449C22×D43—42no—
450C22×D43—81no—
451C22×D43C2×C22⋊C411yescharacteristic
452C22×D43C2×C22⋊C411yescharacteristic
453Q8×C43—21no—
454Q8×C43—21no—
455Q8×C43—21no—
456Q8×C43—42no—
457Q8×C43C4×D412yescomplemented
458D4×C43—22no—
459D4×C43—22no—
460D4×C43—21no—
461D4×C43—21no—
462D4×C43—21no—
463D4×C43—42no—
464D4×C43—42no—
465D4×C43—42no—
466D4×C43—41no—
467D4×C43—41no—
468D4×C43C4×D412yescomplemented
469C2×C4×C43—22no—
470C2×C4×C43—22no—
471C2×C4×C43—21no—
472C2×C4×C43—22no—
473C2×C4×C43—21no—
474C2×C4×C43—21no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—21no—
478C2×C4×C43—21no—
479C2×C4×C43—21no—
480C2×C4×C43—21no—
481C2×C4×C43—22no—
482C2×C4×C43—22no—
483C2×C4×C43—21no—
484C2×C4×C43—21no—
485C2×C4×C43—22no—
486C2×C4×C43—21no—
487C2×C4×C43—42no—
488C2×C4×C43—42no—
489C2×C4×C43—42no—
490C2×C4×C43—48no—
491C2×C4×C43—41no—
492C2×C4×C43—41no—
493C2×C4×C43—41no—
494C2×C4×C43—41no—
495C2×C4×C43C2×C22⋊C411yescharacteristic
496C2×C4×C43C2×C22⋊C411yescharacteristic
497C2×C4×C43C23×C411yescharacteristic
498C2×C4×C43C22×D411yescharacteristic
499C2×C4×C43C22×D411yescharacteristic
500C2×C4×C43C2×#4111yescharacteristic
501C2×C4×C43H(5,𝔽2)11yescharacteristic
502C2×C4×C43H(5,𝔽2)11yescharacteristic
503C22⋊D43—22no—
504C22⋊D43—22no—
505C22⋊D43—22no—
506C22⋊D43—42no—
507C22⋊D43—42no—
508C22⋊D43—41no—
509C22⋊D43—41no—
510C22⋊D43—42no—
511C22⋊D43—42no—
512C22⋊D43—42no—
513C22⋊D43—81no—
514C22⋊D43—81no—
515C22⋊D43—81no—
516C22⋊D43#10414yesdirect product factor
517C2×Dic43—21no—
518C2×Dic43—21no—
519C2×Dic43—22no—
520C2×Dic43—22no—
521C2×Dic43—22no—
522C2×Dic43—21no—
523C2×Dic43—21no—
524C2×Dic43—21no—
525C2×Dic43—41no—
526C2×Dic43—42no—
527C2×Dic43—41no—
528C2×Dic43—41no—
529C2×Dic43—41no—
530C2×Dic43—41no—
531C2×Dic43—42no—
532C2×Dic43—81no—
533C2×Dic43C2×C22⋊C411yescharacteristic
534C2×Dic43C2×C22⋊C411yescharacteristic
535C2×Dic43C2×C22⋊C411yescharacteristic
536C2×Dic43C2×C22⋊C411yescharacteristic
537C2×Dic43C2×C22⋊C411yescharacteristic
538C2×Dic43C2×C22⋊C411yescharacteristic
539D172—21no—
540D172—21no—
541D172—42no—
542C4×D43—21no—
543C4×D43—21no—
544C4×D43—21no—
545C4×D43—21no—
546C4×D43—21no—
547C4×D43—21no—
548C4×D43—21no—
549C4×D43—21no—
550C4×D43—42no—
551C4×D43—42no—
552C4×D43—48no—
553C4×D43—41no—
554C4×D43—41no—
555Dic86—21no—
556Dic86—21no—
557Dic86—42no—
558C8×C43—22no—
559C8×C43—41no—
560C43⋊C8—41no—
561C43⋊C8—41no—
562D4×#104—431nomaximal, Sylow
563C22×C43—21no—
564C22×C43—21no—
565C22×C43—21no—
566C22×C43—21no—
567C22×C43—22no—
568C22×C43—21no—
569C22×C43—21no—
570C22×C43—21no—
571C22×C43—42no—
572C22×C43—42no—
573C22×C43—41no—
574C22×C43—41no—
575C22×C43—41no—
576C22×C43—41no—
577C22×C43—41no—
578C22×C43—84no—
579C22×C43C2×#10412yescomplemented
580C22×C43C22×C22⋊C411yescharacteristic
581C22×C43D4211yescharacteristic
582C22×C43#54611yescharacteristic
583C2×D43—21no—
584C2×D43—21no—
585C2×D43—21no—
586C2×D43—21no—
587C2×D43—21no—
588C2×D43—42no—
589C2×D43—42no—
590C2×D43—41no—
591C2×D43—41no—
592C2×D43—41no—
593C2×D43—84no—
594C2×D43C2×#10412yescomplemented
595C4×C43—24no—
596C4×C43—22no—
597C4×C43—21no—
598C4×C43—21no—
599C4×C43—42no—
600C4×C43—41no—
601C4×C43C2×C4×D411yescharacteristic
602C4×C43#51811yescharacteristic
603C4×C43D4211yescharacteristic
604C4×C43#54611yescharacteristic
605Dic43—21no—
606Dic43—21no—
607Dic43—21no—
608Dic43—21no—
609Dic43—21no—
610Dic43—42no—
611Dic43—42no—
612Dic43—41no—
613Dic43—41no—
614Dic43—41no—
615Dic43C2×#10412yescomplemented
616D4×#41—431no—
617D4×M16—431no—
618C22×#104—431no—
619C22×#104D4311yescharacteristic, complemented
620C42×D4—431no—
621#1980—431no—
622#1962—431no—
623#1896—431no—
624#1896—431no—
625#1871—431no—
626#1871—431no—
627#1806—431no—
628#1789—431no—
629#1789—431no—
630C4×#104—431no—
631C2×C43—21no—
632C2×C43—21no—
633C2×C43—22no—
634C2×C43—42no—
635C2×C43—41no—
636C2×C43—81no—
637C2×C43D4×C22⋊C411yescharacteristic
638C2×C43C22×#10411yescharacteristic
639C2×C43#290111yescharacteristic
640D43—22no—
641D43—41no—
642D43—81no—
643C22×#41—431no—
644C22×#41C2×D4311yescharacteristic
645C22×M16—431no—
646C22×M16C2×D4311yescharacteristic, complemented
647#550—431no—
648D4×Q8—431no—
649#548—431no—
650#548—431no—
651#547—431no—
652#547—861no—
653#546—431no—
654#546—431no—
655#546—861no—
656#546—861no—
657D42—431no—
658D42—861no—
659#532—431no—
660#532—861no—
661#525—431no—
662#525—431no—
663#525—861no—
664#525—861no—
665C4×#41—431no—
666C2×C4×D4—431no—
667C2×C4×D4—861no—
668C2×C4×D4—861no—
669C22×C42—431no—
670C22×C42C2×D4311yescharacteristic, complemented
671#436—861no—
672#435—861no—
673#435—861no—
674C8×D4—861no—
675#423—431no—
676C2×#104—24no—
677C2×#104—431no—
678C2×#104—431no—
679C2×#104—431no—
680C2×#104—431no—
681C2×#104—431no—
682C2×#104—431no—
683C2×#104—431no—
684C2×#104—431no—
685C2×#104—864no—
686C2×#104C2×D4311yescharacteristic
687C2×#104C2×D4311yescharacteristic
688C2×#104C2×D4311yescharacteristic, complemented
689C2×#104C2×D4311yescharacteristic, complemented
690#407—431no—
691#407—431no—
692C4×M16—431no—
693C4×C4⋊C4—431no—
694C4×C4⋊C4—861no—
695C4×C22⋊C4—431no—
696C4×C22⋊C4—431no—
697C4×C22⋊C4—861no—
698C4×C22⋊C4—861no—
699C43—431no—
700#339—431no—
701#339—431no—
702#339—431no—
703#339—431no—
704C43D4×#10411yescharacteristic, complemented, Sylow
705C2×#41—21no—
706C2×#41—21no—
707C2×#41—22no—
708C2×#41—22no—
709C2×#41—41no—
710C2×#41—41no—
711C2×#41—431no—
712C2×#41—431no—
713C2×#41—431no—
714C2×#41—861no—
715C2×#41—861no—
716C2×#41—862no—
717C2×#41—862no—
718C2×#41—1721no—
719C2×#41—1721no—
720C2×#41C4×D4311yescharacteristic, complemented
721C2×#41C4×D4311yescharacteristic, complemented
722C2×#41C22×D4311yescharacteristic
723C2×#41C22×D4311yescharacteristic
724C22×Q8—431no—
725C22×Q8C4×D4311yescharacteristic, complemented
726C22×D4—21no—
727C22×D4—431no—
728C22×D4—431no—
729C22×D4—861no—
730C22×D4—861no—
731C22×D4C4×D4311yescharacteristic, complemented
732C23×C4—21no—
733C23×C4—21no—
734C23×C4—431no—
735C23×C4—861no—
736C23×C4—861no—
737C23×C4C22×D4311yescharacteristic
738C2×M16—21no—
739C2×M16—22no—
740C2×M16—41no—
741C2×M16—431no—
742C2×M16—431no—
743C2×M16—861no—
744C2×M16—862no—
745C2×M16—1721no—
746C2×M16C22×D4311yescharacteristic
747C2×M16C22×D4311yescharacteristic
748C22×C8—21no—
749C22×C8—861no—
750C4⋊Q8—431no—
751C4⋊Q8—861no—
752#127—431no—
753#127—861no—
754#124—431no—
755#124—431no—
756#124—861no—
757#124—861no—
758#123—861no—
759#123—861no—
760#123—861no—
761#123—861no—
762#123—861no—
763#123—861no—
764C22⋊Q8—431no—
765C22⋊Q8—431no—
766C22⋊Q8—431no—
767C22⋊Q8—431no—
768C22⋊Q8—861no—
769C22⋊Q8—861no—
770C22⋊Q8—861no—
771C22⋊Q8—861no—
772#121—431no—
773#121—431no—
774#121—431no—
775#121—431no—
776#121—861no—
777#121—861no—
778#121—861no—
779#121—861no—
780#121—861no—
781#121—861no—
782#121—861no—
783#121—861no—
784#121—861no—
785#121—861no—
786#120—861no—
787#120—861no—
788#120—861no—
789#120—861no—
790#120—861no—
791#120—861no—
792C4×Q8—431no—
793C4×Q8—431no—
794C4×D4—431no—
795C4×D4—431no—
796C4×D4—431no—
797C4×D4—431no—
798C4×D4—431no—
799C4×D4—431no—
800C4×D4—431no—
801C4×D4—431no—
802C4×D4—431no—
803C4×D4—431no—
804C4×D4—861no—
805C4×D4—861no—
806C4×D4—861no—
807C4×D4—861no—
808C4×D4—861no—
809C4×D4—861no—
810C4×D4—861no—
811C4×D4—861no—
812C4×D4—868no—
813C4×D4—861no—
814C4×D4—861no—
815C4×D4—861no—
816C4×D4—861no—
817#117—431no—
818#117—861no—
819C2×C4⋊C4—431no—
820C2×C4⋊C4—861no—
821C2×C4⋊C4—861no—
822C2×C22⋊C4—431no—
823C2×C22⋊C4—431no—
824C2×C22⋊C4—861no—
825C2×C22⋊C4—861no—
826C2×C22⋊C4—861no—
827C2×C22⋊C4—861no—
828C2×C42—22no—
829C2×C42—21no—
830C2×C42—41no—
831C2×C42—431no—
832C2×C42—431no—
833C2×C42—431no—
834C2×C42—861no—
835C2×C42—861no—
836C2×C42—862no—
837C2×C42—861no—
838C2×C42—861no—
839C2×C42—1721no—
840C2×C42C22×D4311yescharacteristic
841C2×C42C22×D4311yescharacteristic
842C4⋊C8—861no—
843C4⋊C8—861no—
844#104—22no—
845#104—22no—
846#104—22no—
847#104—862no—
848#104—862no—
849#104—862no—
850#104—862no—
851#104—1721no—
852#104—1721no—
853#104—1721no—
854#104—1721no—
855#104C22⋊D4314yesdirect product factor
856C22⋊C8—861no—
857C22⋊C8—861no—
858C22⋊C8—861no—
859C22⋊C8—861no—
860#97—861no—
861C4×C8—861no—
862#95—861no—
863#95—861no—
864#95—861no—
865C24—21no—
866C24—431no—
867C24—861no—
868C24D4×D4311yescharacteristic
869#41—21no—
870#41—21no—
871#41—22no—
872#41—22no—
873#41—21no—
874#41—21no—
875#41—21no—
876#41—21no—
877#41—42no—
878#41—42no—
879#41—41no—
880#41—41no—
881#41—42no—
882#41—42no—
883#41—862no—
884#41—862no—
885#41—861no—
886#41—861no—
887#41—861no—
888#41—861no—
889#41—1722no—
890#41—1722no—
891#41—1721no—
892#41—1722no—
893#41—1722no—
894#41—1721no—
895#41#1062189812yes—
896#41C2×C22⋊D4312yes—
897C2×Q8—21no—
898C2×Q8—22no—
899C2×Q8—41no—
900C2×Q8—431no—
901C2×Q8—861no—
902C2×Q8—862no—
903C2×Q8—1721no—
904C2×Q8C2×C4×D4311yescharacteristic
905C2×Q8C2×C4×D4311yescharacteristic
906C2×D4—21no—
907C2×D4—22no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—41no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—431no—
916C2×D4—431no—
917C2×D4—431no—
918C2×D4—431no—
919C2×D4—431no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—861no—
923C2×D4—861no—
924C2×D4—864no—
925C2×D4—862no—
926C2×D4—861no—
927C2×D4—861no—
928C2×D4—861no—
929C2×D4—861no—
930C2×D4—861no—
931C2×D4—861no—
932C2×D4—1721no—
933C2×D4—1722no—
934C2×D4—1722no—
935C2×D4—1724no—
936C2×D4C2×C4×D4311yescharacteristic
937C2×D4C2×C4×D4311yescharacteristic
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—24no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—431no—
955C22×C4—431no—
956C22×C4—431no—
957C22×C4—431no—
958C22×C4—431no—
959C22×C4—431no—
960C22×C4—431no—
961C22×C4—861no—
962C22×C4—861no—
963C22×C4—864no—
964C22×C4—861no—
965C22×C4—861no—
966C22×C4—861no—
967C22×C4—861no—
968C22×C4—861no—
969C22×C4—861no—
970C22×C4—861no—
971C22×C4—861no—
972C22×C4—861no—
973C22×C4—861no—
974C22×C4—1722no—
975C22×C4—1722no—
976C22×C4—1722no—
977C22×C4—1722no—
978C22×C4C2×C4×D4311yescharacteristic
979C22×C4C2×C4×D4311yescharacteristic
980C22×C4D4×D4311yescharacteristic
981C22×C4D4×D4311yescharacteristic
982C22×C4D4×D4311yescharacteristic
983C22×C4C23×D4311yescharacteristic
984M16—21no—
985M16—21no—
986M16—21no—
987M16—42no—
988M16—861no—
989M16—861no—
990M16—861no—
991M16—861no—
992M16—1722no—
993M16C2×C22⋊D4312yescomplemented
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—42no—
997C2×C8—861no—
998C2×C8—861no—
999C2×C8—1722no—
1000C4⋊C4—431no—
1001C4⋊C4—431no—
1002C4⋊C4—431no—
1003C4⋊C4—431no—
1004C4⋊C4—431no—
1005C4⋊C4—431no—
1006C4⋊C4—861no—
1007C4⋊C4—861no—
1008C4⋊C4—861no—
1009C4⋊C4—861no—
1010C4⋊C4—861no—
1011C4⋊C4—861no—
1012C4⋊C4—864no—
1013C4⋊C4—861no—
1014C4⋊C4—861no—
1015C22⋊C4—431no—
1016C22⋊C4—431no—
1017C22⋊C4—431no—
1018C22⋊C4—431no—
1019C22⋊C4—431no—
1020C22⋊C4—431no—
1021C22⋊C4—431no—
1022C22⋊C4—431no—
1023C22⋊C4—861no—
1024C22⋊C4—861no—
1025C22⋊C4—861no—
1026C22⋊C4—861no—
1027C22⋊C4—864no—
1028C22⋊C4—861no—
1029C22⋊C4—861no—
1030C22⋊C4—861no—
1031C22⋊C4—861no—
1032C22⋊C4—861no—
1033C22⋊C4—861no—
1034C22⋊C4—864no—
1035C22⋊C4—861no—
1036C22⋊C4—861no—
1037C22⋊C4—861no—
1038C22⋊C4—861no—
1039C22⋊C4—861no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—42no—
1044C42—431no—
1045C42—431no—
1046C42—431no—
1047C42—431no—
1048C42—861no—
1049C42—861no—
1050C42—864no—
1051C42—861no—
1052C42—861no—
1053C42—861no—
1054C42—861no—
1055C42—861no—
1056C42—1722no—
1057C42—1722no—
1058C42C2×C22⋊D4312yescomplemented
1059C23—21no—
1060C23—22no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—81no—
1068C23—431no—
1069C23—431no—
1070C23—862no—
1071C23—861no—
1072C23—861no—
1073C23—861no—
1074C23—3441no—
1075C23—1721no—
1076C23—1722no—
1077C23—1722no—
1078C23C22⋊C4×D4311yescharacteristic
1079C23C22⋊C4×D4311yescharacteristic
1080C23C2×D4×D4311yescharacteristic
1081Q8—21no—
1082Q8—21no—
1083Q8—21no—
1084Q8—42no—
1085Q8—861no—
1086Q8—861no—
1087Q8—1722no—
1088Q8C4×C22⋊D4312yescomplemented
1089D4—22no—
1090D4—22no—
1091D4—21no—
1092D4—21no—
1093D4—21no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—41no—
1098D4—41no—
1099D4—434no—
1100D4—862no—
1101D4—862no—
1102D4—862no—
1103D4—861no—
1104D4—861no—
1105D4—3441no—
1106D4—3441no—
1107D4—3441no—
1108D4—1722no—
1109D4—1722no—
1110D4—1722no—
1111D4—1722no—
1112D4—1722no—
1113D4—1722no—
1114D4—1721no—
1115D4—1721no—
1116D4C4×C22⋊D4312yescomplemented
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—48no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—431no—
1144C2×C4—431no—
1145C2×C4—431no—
1146C2×C4—431no—
1147C2×C4—431no—
1148C2×C4—431no—
1149C2×C4—862no—
1150C2×C4—861no—
1151C2×C4—861no—
1152C2×C4—861no—
1153C2×C4—861no—
1154C2×C4—861no—
1155C2×C4—861no—
1156C2×C4—861no—
1157C2×C4—861no—
1158C2×C4—861no—
1159C2×C4—861no—
1160C2×C4—862no—
1161C2×C4—862no—
1162C2×C4—861no—
1163C2×C4—861no—
1164C2×C4—861no—
1165C2×C4—3441no—
1166C2×C4—1722no—
1167C2×C4—1722no—
1168C2×C4—1728no—
1169C2×C4—1722no—
1170C2×C4—1721no—
1171C2×C4—1722no—
1172C2×C4—1721no—
1173C2×C4—1721no—
1174C2×C4—1721no—
1175C2×C4—1721no—
1176C2×C4—1721no—
1177C2×C4—1721no—
1178C2×C4C22⋊C4×D4311yescharacteristic
1179C2×C4C22⋊C4×D4311yescharacteristic
1180C2×C4C22×C4×D4311yescharacteristic
1181C2×C4C2×D4×D4311yescharacteristic
1182C2×C4C22×C22⋊D4311yescharacteristic
1183C2×C4C2×#1062189811yescharacteristic
1184C2×C4#1306337011yescharacteristic
1185C2×C4#1306337011yescharacteristic
1186C8—22no—
1187C8—41no—
1188C8—1721no—
1189C8—1721no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—21no—
1194C22—21no—
1195C22—22no—
1196C22—21no—
1197C22—21no—
1198C22—42no—
1199C22—42no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—84no—
1206C22—432no—
1207C22—861no—
1208C22—861no—
1209C22—861no—
1210C22—861no—
1211C22—861no—
1212C22—3444no—
1213C22—1722no—
1214C22—1722no—
1215C22—1721no—
1216C22—1721no—
1217C22—1721no—
1218C22#104×D4312yescomplemented
1219C22C2×C22⋊C4×D4311yescharacteristic
1220C22D4×C22⋊D4311yescharacteristic
1221C22#1458353911yescharacteristic
1222C4—24no—
1223C4—21no—
1224C4—21no—
1225C4—22no—
1226C4—42no—
1227C4—41no—
1228C4—432no—
1229C4—861no—
1230C4—861no—
1231C4—861no—
1232C4—861no—
1233C4—861no—
1234C4—1722no—
1235C4—1722no—
1236C4—1721no—
1237C4—1721no—
1238C4—1721no—
1239C4C2×C4×C22⋊D4311yescharacteristic
1240C4#1458337211yescharacteristic
1241C4D4×C22⋊D4311yescharacteristic
1242C4#1458353911yescharacteristic
1243C2—21no—
1244C2—21no—
1245C2—22no—
1246C2—41no—
1247C2—42no—
1248C2—81no—
1249C2—862no—
1250C2—3441no—
1251C2—1721no—
1252C2C22⋊C4×C22⋊D4311yescharacteristic
1253C2C2×#104×D4311yescharacteristic
1254C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#104×C43C2
socleC22×C43C22×C22⋊C4
prime radical#41×C22⋊D43C2
cosocleC22×C4×C43C24
hypercenterC22×#104D43
hypocenterC43D4×#104
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. M16×C22⋊D43C2semidirect
3. C2×#104×D43C2semidirect
4. C42×C22⋊D43C2semidirect
5. #19135512C2semidirect
6. #19135421C2semidirect
7. #19135038C2semidirect
8. #19135035C2semidirect
9. #19134897C2semidirect
10. #19134894C2semidirect
11. #19134613C2semidirect
12. #19134539C2semidirect
13. #19134537C2semidirect
14. #104×Dic43C2semidirect
15. C22×#104×C43C2semidirect
17. C2×M16×D43C22semidirect
18. #14583568C4semidirect
19. Q8×C22⋊D43C4semidirect
20. #14583560C4semidirect
21. #14583556C4semidirect
23. #14583548C4semidirect
25. #14583543C4semidirect
27. #14583537C4semidirect
29. D4×C22⋊D43C4semidirect
40. C2×C42×D43C22semidirect
45. #14582922C22semidirect
46. C2×#13063253C22semidirect
47. C2×#13063253C22semidirect
50. C2×#13063252C22semidirect
51. C2×#13063252C22semidirect
52. C2×#13063251C22semidirect
53. C2×#13063251C22semidirect
55. #14582863C22semidirect
56. #14582862C22semidirect
57. M16×Dic43C22semidirect
59. C4×Dic43⋊C4C22semidirect
61. C4×(C2×D43)⋊C4C22semidirect
63. C4×C22⋊Dic43C22semidirect
64. C42×Dic43C22semidirect
65. #14582660C22semidirect
66. #14582660C22semidirect
67. #14582659C22semidirect
68. #14582659C22semidirect
70. C22×M16×C43C22semidirect
71. C22×C42×C43C22semidirect
75. C2×#104×C43C22semidirect
76. C2×#104×C43C22semidirect
77. C2×#10621902C2×C4semidirect
81. C2×#10621900C2×C4semidirect
86. C2×Q8×D43C2×C4semidirect
90. C2×D4×D43C2×C4semidirect
101. #13063323C2×C4semidirect
103. #13063321C2×C4semidirect
105. #13063314C2×C4semidirect
107. #13063312C2×C4semidirect
116. #13063304C2×C4semidirect
117. #13063304C2×C4semidirect
120. #13063301C2×C4semidirect
121. #13063301C2×C4semidirect
124. #13063299C2×C4semidirect
125. #13063299C2×C4semidirect
134. #13063296C2×C4semidirect
135. #13063296C2×C4semidirect
142. Q8×Dic43C2×C4semidirect
143. Q8×Dic43C2×C4semidirect
146. D4×Dic43C2×C4semidirect
147. D4×Dic43C2×C4semidirect
212. C2×#41×C43C2×C4semidirect
213. C2×#41×C43C2×C4semidirect
216. C22×Q8×C43C2×C4semidirect
218. C22×D4×C43C2×C4semidirect
236. #104×C43D4semidirect
360. M16×C43C2×D4semidirect
368. C42×C43C2×D4semidirect
457. Q8×C43C4×D4semidirect
468. D4×C43C4×D4semidirect
516. C22⋊D43#104direct (N × H)
579. C22×C43C2×#104semidirect
594. C2×D43C2×#104semidirect
615. Dic43C2×#104semidirect
619. C22×#104D43semidirect
646. C22×M16C2×D43semidirect
670. C22×C42C2×D43semidirect
688. C2×#104C2×D43semidirect
689. C2×#104C2×D43semidirect
704. C43D4×#104semidirect
720. C2×#41C4×D43semidirect
721. C2×#41C4×D43semidirect
725. C22×Q8C4×D43semidirect
731. C22×D4C4×D43semidirect
855. #104C22⋊D43direct (N × H)
993. M16C2×C22⋊D43semidirect
1058. C42C2×C22⋊D43semidirect
1088. Q8C4×C22⋊D43semidirect
1116. D4C4×C22⋊D43semidirect
1218. C22#104×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#41×C22⋊D432
M16×C22⋊D432
C2×#104×D432
C42×C22⋊D432
#191355122
#191354212
#191350382
#191350352
#191348972
#191348942
#191346132
#191345392
#191345372
#104×Dic432
C22×#104×C432
D4×#10443